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Journal ArticleDOI

The electronic properties of graphene

TL;DR: In this paper, the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations, are discussed.
Abstract: This article reviews the basic theoretical aspects of graphene, a one-atom-thick allotrope of carbon, with unusual two-dimensional Dirac-like electronic excitations. The Dirac electrons can be controlled by application of external electric and magnetic fields, or by altering sample geometry and/or topology. The Dirac electrons behave in unusual ways in tunneling, confinement, and the integer quantum Hall effect. The electronic properties of graphene stacks are discussed and vary with stacking order and number of layers. Edge (surface) states in graphene depend on the edge termination (zigzag or armchair) and affect the physical properties of nanoribbons. Different types of disorder modify the Dirac equation leading to unusual spectroscopic and transport properties. The effects of electron-electron and electron-phonon interactions in single layer and multilayer graphene are also presented.

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Citations
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Journal ArticleDOI
TL;DR: In this paper, a brief overview of the electronic and transport properties of graphene nanoribbons focusing on the effect of edge shapes and impurity scattering is presented, where two valleys related to each Dirac spectrum are well separated in momentum space.
Abstract: We will present a brief overview of the electronic and transport properties of graphene nanoribbons focusing on the effect of edge shapes and impurity scattering. The low-energy electronic states of graphene have two non-equivalent massless Dirac spectra. The relative distance between these two Dirac points in the momentum space and edge states due to the existence of zigzag-type graphene edges is a deciding factor in the electronic and transport properties of graphene nanoribbons. In graphene nanoribbons with zigzag edges (zigzag nanoribbons), two valleys related to each Dirac spectrum are well separated in momentum space. The propagating modes in each valley contain a single chiral mode originating from a partially flat band at the band center. This feature gives rise to a perfectly conducting channel in the disordered system, if impurity scattering does not connect the two valleys, i.e. for long-range impurity (LRI) potentials. Ribbons with short-range impurity potentials, however, display ordinary localization behavior through inter-valley scattering. On the other hand, the low-energy spectrum of graphene nanoribbons with armchair edges (armchair nanoribbons) is described as the superposition of two non-equivalent Dirac points of graphene. In spite of the lack of two well separated valley structures, the single-channel transport subjected to LRIs is nearly perfectly conducting, where the backward scattering matrix elements in the lowest order vanish as a manifestation of internal phase structures of the wave function. For the multi-channel energy regime, however, conventional exponential decay of the averaged conductance occurs. Symmetry considerations lead to the classification of disordered zigzag ribbons into the unitary class for LRIs, and the orthogonal class for short-range impurities. Since inter-valley scattering is not completely absent, armchair nanoribbons can be classified into the orthogonal universality class irrespective of the range of impurities.

198 citations

Journal ArticleDOI
11 Oct 2011-ACS Nano
TL;DR: A systematic experimental and theoretical analysis of the Raman modes in bothBernal (ABA stacking order) and rhombohedral trilayer graphene (3LG) shows that the G band, G' (2D) band, and the intermediate-frequency combination modes of 3LGs are sensitive to the stacking order of 3LG.
Abstract: Bernal (ABA stacking order) and rhombohedral (ABC) trilayer graphene (3LG) are characterized by Raman spectroscopy. From a systematic experimental and theoretical analysis of the Raman modes in both of these 3LGs, we show that the G band, G' (2D) band, and the intermediate-frequency combination modes of 3LGs are sensitive to the stacking order of 3LG. The phonon wavevector q, that gives the double resonance Raman spectra is larger in ABC than ABA, which is the reason why we get the different Raman frequencies and their spectral widths for ABA and ABC 3LG. The weak electron-phonon interaction in ABC-stacked 3LG and the localized strain at the boundary between ABC- and ABA-stacked domains are clearly reflected by the softening of the G mode and the G' mode, respectively.

197 citations

Journal ArticleDOI
TL;DR: The structural, electronic and vibrational properties of free-standing silicene, as predicted from first-principles calculations are discussed, providing insights into the different phases or atomic arrangements ofsilicene observed on this metallic surface, as well as on its electronic structure.
Abstract: Silicene is the silicon counterpart of graphene, i.e. it consists in a single layer of Si atoms with a hexagonal arrangement. We present a review of recent theoretical and experimental works on this novel two dimensional material. We discuss first the structural, electronic and vibrational properties of free-standing silicene, as predicted from first-principles calculations. We next review theoretical studies on the interaction of silicene with different substrates. The growth and experimental characterization of silicene on Ag(1 1 1) is next discussed, providing insights into the different phases or atomic arrangements of silicene observed on this metallic surface, as well as on its electronic structure. Recent experimental findings about the likely formation of hexagonal Si nanosheets on MoS2 are also highlighted.

197 citations

Journal ArticleDOI
TL;DR: In this paper, the sensitivity of pristine graphene (PG) and Pd-doped graphene (Pd-G) toward a series of small gas molecules (CO, NH 3, O 2 and NO 2 ) has been investigated by first-principles based on density functional theory.

197 citations


Additional excerpts

  • ...It is worth entioning that the electronic state of graphene near the Dirac oint shows linear energy dispersion and zero band gap [6]....

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  • ...[6] A....

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  • ...Graphene, a one-atom-thick carbon honeycomb structure, has ttracted considerable attention due to its intriguing electric and ransport properties since its discovery in 2004 [1–6]....

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Journal ArticleDOI
25 Apr 2011-ACS Nano
TL;DR: This work indicates that graphene can be grown with a perfect continuity extending over both crystalline and noncrystalline regions, highly suggestive of weak graphene-substrate interactions.
Abstract: Understanding of the continuity and the microscopic structure of as-grown graphene on Cu foils through the chemical vapor deposition (CVD) method is of fundamental significance for optimizing the growth parameters toward high-quality graphene. Because of the corrugated nature of the Cu foil surface, few experimental efforts on this issue have been made so far. We present here a high-resolution scanning tunneling microscopy (STM) study of CVD graphene directly on Cu foils. Our work indicates that graphene can be grown with a perfect continuity extending over both crystalline and noncrystalline regions, highly suggestive of weak graphene–substrate interactions. Due to thermal expansion mismatch, defect-like wrinkles and ripples tend to evolve either along the boundaries of crystalline terraces or on noncrystalline areas for strain relief. Furthermore, the strain effect arising from the conforming of perfect two-dimensional graphene to the highly corrugated surface of Cu foils is found to induce local bondin...

196 citations

References
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Journal ArticleDOI
22 Oct 2004-Science
TL;DR: Monocrystalline graphitic films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands and they exhibit a strong ambipolar electric field effect.
Abstract: We describe monocrystalline graphitic films, which are a few atoms thick but are nonetheless stable under ambient conditions, metallic, and of remarkably high quality. The films are found to be a two-dimensional semimetal with a tiny overlap between valence and conductance bands, and they exhibit a strong ambipolar electric field effect such that electrons and holes in concentrations up to 10 13 per square centimeter and with room-temperature mobilities of ∼10,000 square centimeters per volt-second can be induced by applying gate voltage.

55,532 citations


"The electronic properties of graphe..." refers background in this paper

  • ...Be ause the DC magnetotransport properties ofgraphene are normally measured with the possibilityof tuning its ele troni density by a gate potential(Novoselov et al., 2004), it is important to ompute the ondu tivity kernel, sin e this has dire t experimentalrelevan e....

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  • ...The same polarizability describes the screening of an external field perpendicular to the layers, like the one induced by a gate in electrically doped systems (Novoselov et al., 2004)....

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  • ...Because the DC magnetotransport properties of graphene are normally measured with the possibility of tuning its electronic density by a gate potential (Novoselov et al., 2004), it is important to compute the conductivity kernel, since this has direct experimental relevance....

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  • ...…studies of graphene sta ks have showed that, within reasing number of layers, the system be omes in reas-ingly metalli ( on entration of harge arriers at zero en-ergy gradually in reases), and there appear several typesof ele tron-and-hole-like arries (Morozov et al., 2005;Novoselov et al., 2004)....

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  • ...The same polarizabilitydes ribes the s reening of an external eld perpendi ularto the layers, like the one indu ed by a gate in ele tri- ally doped systems (Novoselov et al., 2004)....

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Journal ArticleDOI
TL;DR: Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena can now be mimicked and tested in table-top experiments.
Abstract: Graphene is a rapidly rising star on the horizon of materials science and condensed-matter physics. This strictly two-dimensional material exhibits exceptionally high crystal and electronic quality, and, despite its short history, has already revealed a cornucopia of new physics and potential applications, which are briefly discussed here. Whereas one can be certain of the realness of applications only when commercial products appear, graphene no longer requires any further proof of its importance in terms of fundamental physics. Owing to its unusual electronic spectrum, graphene has led to the emergence of a new paradigm of 'relativistic' condensed-matter physics, where quantum relativistic phenomena, some of which are unobservable in high-energy physics, can now be mimicked and tested in table-top experiments. More generally, graphene represents a conceptually new class of materials that are only one atom thick, and, on this basis, offers new inroads into low-dimensional physics that has never ceased to surprise and continues to provide a fertile ground for applications.

35,293 citations


"The electronic properties of graphe..." refers background in this paper

  • ...As the current status of the experiment and potential applications have recently been reviewed (Geim and Novoselov, 2007), in this article we mostly concentrate on the theory and more technical aspects of electronic properties of this exciting new material....

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  • ...As the urrent status of the experimentand potential appli ations have re ently been reviewed(Geim and Novoselov, 2007), in this arti le we mostly on entrate on the theory and more te hni al aspe ts ofele troni properties of this ex iting new material....

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  • ...It has also been suggested that Coulomb intera tionsare onsiderably enhan ed in smaller geometries, su has graphene quantum dots (Milton Pereira Junior et al.,2007), leading to unusual Coulomb blo kade e e ts 4(Geim and Novoselov, 2007) and perhaps to magneti phenomena su h as the Kondo e e t....

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  • ...…most versatile systems in ondensedmatter resear h.Besides the unusual basi properties, graphene hasthe potential for a large number of appli ations(Geim and Novoselov, 2007), from hemi al sensors(Chen et al., 2007 ; S hedin et al., 2007) to transistors(Nilsson et al., 2007b; Oostinga et al.,…...

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  • ...Besides the unusual basic properties, graphene has the potential for a large number of applications (Geim and Novoselov, 2007), from chemical sensors (Chen et al....

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Book
01 Jan 1934
TL;DR: The theory of the slipline field is used in this article to solve the problem of stable and non-stressed problems in plane strains in a plane-strain scenario.
Abstract: Chapter 1: Stresses and Strains Chapter 2: Foundations of Plasticity Chapter 3: Elasto-Plastic Bending and Torsion Chapter 4: Plastic Analysis of Beams and Frames Chapter 5: Further Solutions of Elasto-Plastic Problems Chapter 6: Theory of the Slipline Field Chapter 7: Steady Problems in Plane Strain Chapter 8: Non-Steady Problems in Plane Strain

20,724 citations

Journal ArticleDOI
10 Nov 2005-Nature
TL;DR: This study reports an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation and reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions.
Abstract: Quantum electrodynamics (resulting from the merger of quantum mechanics and relativity theory) has provided a clear understanding of phenomena ranging from particle physics to cosmology and from astrophysics to quantum chemistry. The ideas underlying quantum electrodynamics also influence the theory of condensed matter, but quantum relativistic effects are usually minute in the known experimental systems that can be described accurately by the non-relativistic Schrodinger equation. Here we report an experimental study of a condensed-matter system (graphene, a single atomic layer of carbon) in which electron transport is essentially governed by Dirac's (relativistic) equation. The charge carriers in graphene mimic relativistic particles with zero rest mass and have an effective 'speed of light' c* approximately 10(6) m s(-1). Our study reveals a variety of unusual phenomena that are characteristic of two-dimensional Dirac fermions. In particular we have observed the following: first, graphene's conductivity never falls below a minimum value corresponding to the quantum unit of conductance, even when concentrations of charge carriers tend to zero; second, the integer quantum Hall effect in graphene is anomalous in that it occurs at half-integer filling factors; and third, the cyclotron mass m(c) of massless carriers in graphene is described by E = m(c)c*2. This two-dimensional system is not only interesting in itself but also allows access to the subtle and rich physics of quantum electrodynamics in a bench-top experiment.

18,958 citations


"The electronic properties of graphe..." refers background or methods in this paper

  • ...This amazing re-sult has been observed experimentally (Novoselov et al.,2005a; Zhang et al., 2005) as shown in Fig.20....

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  • ...Adapted from(Novoselov et al., 2005a)....

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  • ...Adapted from (Novoselov et al.,2005a).and hen e σxy,inc. = I/VH = ±4Ne2/h, whi h is thenaive expe tation....

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  • ...The period of os illations ∆n = 4B/Φ0,where B is the applied eld and Φ0 is the ux quantum(Novoselov et al., 2005a).or equivalently: (Oσ+ + O†σ−)φ = (2E/ωc)φ , (100)where σ± = σx ± iσy, and we have de ned the dimen-sionless length s ale: ξ = y ℓB − ℓBk , (101)and 1D harmoni os illator operators: O =…...

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  • ...…invery unusual ways when ompared to ordinary ele tronsif subje ted to magneti elds, leading to new physi alphenomena (Gusynin and Sharapov, 2005; Peres et al.,2006 ) su h as the anomalous integer quantum Hall ef-fe t (IQHE) measured experimentally (Novoselov et al.,2005a; Zhang et al., 2005)....

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Book
01 Jan 1939

14,299 citations